I'm not sure you need a jre. If I were to guess I'd say no, but it's been awhile since I played with applets on computers who didn't have it installed.
But web games are better for a host of other reasons:
- compatibility between os-es
- compatibility between versions of the same OS (win 95 vs xp) - much greater lifetime
- no hassle with installs, play instantly and from anywhere
You have a default jre installed in the browser for 10 years already. The problem is it's not always the right version or flavor - Microsoft did a lot of nasty stuff in this direction. But this was a long time ago, that's why I said these days you probably don't need a separate download.
As an up to date example, I tried a yahoo card game this week-end (http://games.yahoo.com/card-games), and I couldn't launch the game in FF without installing the latest JRE plugin. The game in question if you wanna try is "pyramids".
But web games are better for a host of other reasons:
- compatibility between os-es
- compatibility between versions of the same OS (win 95 vs xp) - much greater lifetime
- no hassle with installs, play instantly and from anywhere
- easier to multiplay
- switch from "savegames" to a "profile".